Generalized Contraction and Invariant Approximation Results on Nonconvex Subsets of Normed Spaces

Abstract EN

Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle.

In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces.

Some theorems on invariant approximations in normed linear spaces are also deduced.

Our results extend, unify, and generalize comparable results in the literature.